How Trading Costs Shape Equilibrium Returns and Liquidity Premia

Summary

This paper analyzes risk-sharing equilibria when agents face convex costs on their trading rates. In an infinite-horizon model with linear state dynamics and exogenous volatility, equilibrium returns move around their frictionless values. With quadratic costs, the deviation follows Ornstein–Uhlenbeck dynamics; with proportional costs, it follows a doubly reflected Brownian motion. More general settings with arbitrary state dynamics and endogenous volatility produce coupled nonlinear forward-backward systems.

For those harder cases, the authors describe a simulation-based deep-learning method for numerical solutions. A calibration to price and volume time series produces liquidity premia alongside a moderate rise in volatility. The reported effects are similar across cost specifications, supporting quadratic costs as a tractable proxy. The supplied text gives no calibration details or quantitative estimates of the premia, and the numerical method is presented for models outside established well-posedness results. These findings concern modeled equilibrium behavior, not a direct trading strategy or proof of realized returns.

Key ideas

• Trading costs cause equilibrium returns to deviate from their frictionless counterparts.
• Quadratic costs produce Ornstein–Uhlenbeck dynamics for the return deviation in the specified model.
• Proportional costs produce a doubly reflected Brownian motion for that deviation.
• More general models require numerical methods for coupled nonlinear forward-backward systems.
• The calibration associates liquidity premia with a moderate increase in volatility and finds broadly similar effects across cost specifications.

Tags

# Asset Pricing with General Transaction Costs: Theory and Numerics


# Asset Pricing with General Transaction Costs: Theory and Numerics









We study risk-sharing equilibria with general convex costs on the agents' trading rates. For an infinite-horizon model with linear state dynamics and exogenous volatilities, we prove that the equilibrium returns mean-revert around their frictionless counterparts - the deviation has Ornstein-Uhlenbeck dynamics for quadratic costs whereas it follows a doubly-reflected Brownian motion if costs are proportional. More general models with arbitrary state dynamics and endogenous volatilities lead to multidimensional systems of nonlinear, fully-coupled forward-backward SDEs. These fall outside the scope of known wellposedness results, but can be solved numerically using the simulation-based deep-learning approach of Han, Jentzen and E (2018). In a calibration to time series of prices and trading volume, realistic liquidity premia are accompanied by a moderate increase in volatility. The effects of different cost specifications are rather similar, justifying the use of quadratic costs as a proxy for other less tractable specifications.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.